Introduction to Mathematical Structures an...

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Sprache: Englisch

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Beschreibung

As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor¿and the flexible thinking¿required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader.
The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on [...] forinstructors adopting the text for a course.

Über den Autor

Larry Gerstein's primary areas of research have been in quadratic forms and number theory and he has published extensively in these areas. The author's first edition of "Introduction to Mathematical Structures and Proofs" has sold to date (8/2/2010) over 6000 copies and has gone through 5 printings. Gerstein himself has a transition course at UC, Santa Barbara (Math 8-A transition to higher mathematics) from his book since its first publication date. The first edition also received 2 glowing reviews by Steve Krantz for the American Mathematical Monthly, and S. Gottwald for Zentralblatt.

Zusammenfassung

Solutions manual for even numbered exercises is available on [...] for instructors adopting the text for a course

Discusses the multifaceted process of mathematical proof by thoughtful oscillation between what is known and what is to be demonstrated

Presents more than one proof for many results, for instance for the fact that there are infinitely many prime numbers

Shows how the processes of counting and comparing the sizes of finite sets are based in function theory, and how the ideas can be extended to infinite sets via Cantor's theorems

Contains a wide assortment of exercises, ranging from routine checks of a student's grasp of definitions through problems requiring more sophisticated mastery of fundamental ideas

Demonstrates the dual importance of intuition and rigor in the development of mathematical ideas

Request lecturer material: [...]

Inhaltsverzeichnis

Preface to the Second Edition.- Preface to the First Edition.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.- 5. Combinatorics.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index.

Details

Erscheinungsjahr:	2016
Fachbereich:	Grundlagen
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xiii 401 S.
ISBN-13:	9781493951468
ISBN-10:	1493951467
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Gerstein, Larry J.
Auflage:	Softcover reprint of the original 2nd ed. 2012
Hersteller:	Springer New York Springer US, New York, N.Y. Undergraduate Texts in Mathematics
Maße:	254 x 178 x 23 mm
Von/Mit:	Larry J. Gerstein
Erscheinungsdatum:	23.08.2016
Gewicht:	0,779 kg

Artikel-ID: 109582478